The unlikely starting point for Britain’s transformation into a country of electrical highways is a shop in White City’s Westfield shopping centre, next to a Diesel clothing outlet on the first floor. This is the only place that motorists with cash to burn can buy the Tesla Model S, said to be the car that will finally launch us into an electric future of quiet, clean, environmental motoring, where Londoners will be able to ferry their family to the Pennines of a bank holiday weekend without using a drip of petrol — or slowing down much either. If this shop does well in the coming months, the technology it sells could put be putting a dent in London’s pollution and carbon emissions within years. If it doesn’t, the world’s most ambitious billionaire will have egg on his face.

South African-born Elon Musk, 42, who made much of his fortune through the co-founding and sale of PayPal, is coming to London in two weeks to hand over a Model S to the first five customers. The staff in his very unusual dealership (they’re in open-necked white shirts, distressed jeans and boots) say that since opening in October they have sold to all sorts — some of whom have flown in for a test drive from Scotland, Portugal and Singapore.

As I enter, sales rep Ross is telling a few young Asian men about the car, which is an executive estate, available for £70,000, with the highest-ever safety assessment in North America (“We actually broke some of their testing equipment”). It has an enormous boot space under the bonnet and enough space in the rear boot for two backwards-facing child seats. On the wall a screen lets customers work out how much they’d save on fuel (more than £3,000 a year if you drive 25,000km ). He lets me drive it around west London, so I believe him about the “incredible torque” and that this is the first “performance” electric car. Inside it has lots of James Bond features, such as a laptop-sized flat screen on which you can browse Facebook alongside the sat nav. It’s very quiet — only growling when I put my foot down going up a motorway ramp.

Already the third-bestselling luxury car in California, the Model S is a full-sized five-door liftback whose great hopes lie in its 85kWh lithium-ion battery pack, which gives it the greatest range (claimed to be 312 miles) of any electric car to date. Buyers started driving it in northern Europe — including Norway, Switzerland and the Netherlands — at the end of last year, and it has been met with very positive reviews.

The company hopes the handover ceremony will be the moment that electric cars become a serious proposition in this country, after several false starts and much Government patronage.

The car has been on sale at Westfield since the shop opened in October and the early customers (including those who have been making online reservations going back years) will be taking delivery of their cars next month, though Tesla won’t say how many they have actually sold. “People are very interested in the car,” a spokesman told the Standard. “I think it surprises people that you can have such performance from an electric car, that it rivals non-electric vehicles.”

One of the challenges for Musk is reaching people beyond green enthusiasts. The Tesla spokesman says: “It’s a real range of people — some of them are environmentally aware, some of them are car nuts, some of them are tech types — it’s a real mixed bag.”

Musk’s ambition to overcome the “range anxiety” that has held back the sales of electric cars has seen Tesla turn major roads in the US and northern Europe into “supercharger highways” — dotted with express-charging stations for their vehicles outside major cities so drivers can make long trips.

London users can charge their cars overnight with normal home-charging stations, or during a meal or while at work. The superchargers power the car up much faster, giving it half a charge (more than 150 miles of driving) after a 20-minute plug-in.

The “highway” — expected to be operational by the end of the year — will stretch down the M1 from the North to London, and off towards Bristol on the M4 and Dover on the M20, where users can then effectively join the European network. It was reported this weekend that construction of the UK stations is almost complete, with one located at South Mimms services, at the junction of the M25 and the A1 in Hertfordshire. An interactive map on the Tesla website shows how the company intends to expand dramatically the highways across Europe, with the highest concentration of stations in Norway, Germany, France, Italy and the Netherlands.

The company, founded in 2003, has been described by Bloomberg as “an automotive phenomenon” and is worth more than £24 billion. Its share price surged last year when it announced its first quarterly profit and the Model S received ecstatic reviews, including from US car magazine Consumer Reports, which named it 2014’s “best overall” car and called it a “technological tour de force”.

Much of the company’s momentum — and its mystique — comes courtesy of Musk’s involvement. After joining as an investor in 2004, he took over as CEO in 2008 and is thought to own a 32 per cent stake, worth $18 billion.

Musk is the fastest-moving billionaire on the planet, the kind of mogul usually imagined by film directors, but in Musk’s case he’s the inspiration for them. The billionaire industrialist Tony Stark played by Robert Downey Jr in the Iron Man films is based on Musk, and parts of Iron Man 2 were shot inside the futuristic headquarters of his space company SpaceX. Following successful rocket tests in April, SpaceX said yesterday it was making “progress” in its aim of establishing a colony on Mars by 2020, and says it plans to sell tickets for £296,900 a trip. Getting passengers to Mars was Musk’s stated objective when he started the company, though its ambitions have expanded since then. He now envisions a colony of 80,000 humans on the red planet.

Musk was married to Canadian sci-fi writer Justine Wilson, with whom he has five sons, until 2008. He is thought to be back with his second wife, British actress Talulah Riley, 28, whom he married six years ago. In 2012 he seemed to have ended the relationship, tweeting: “It was an amazing four years. I will love you for ever. You will make someone very happy one day.” But he took Riley to a White House dinner in February and told an interviewer they were back on.

She is expected to join him in London for the launch. After which we might be seeing more of rocket man Elon Musk.